Tiffany is 20 years older than Stephanie. Nineteen years ago, Tiffany was 3 times as old as Stephanie. How old is Stephanie now?
Answer: We can use the given information to write down two equations that describe the ages of Tiffany and Stephanie. Let Tiffany's current age be $t$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $t = s + 20$ Nineteen years ago, Tiffany was $t - 19$ years old, and Stephanie was $s - 19$ years old. The information in the second sentence can be expressed in the following equation: $t - 19 = 3(s - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to use our first equation for $t$ and substitute it into our second equation. Our first equation is: $t = s + 20$ . Substituting this into our second equation, we get the equation: $(s + 20)$ $-$ $19 = 3(s - 19)$ which combines the information about $s$ from both of our original equations. Simplifying both sides of this equation, we get: $s + 1 = 3 s - 57$ Solving for $s$ , we get: $2 s = 58$ $s = 29$.